Topological Phase Transitions in Line-nodal Superconductors

Fathoming interplay between symmetry and topology of many-electron wave-functions has deepened understanding of quantum many body systems, especially after the discovery of topological insulators. Topology of electron wave-functions enforces and protects emergent gapless excitations, and symmetry is intrinsically tied to the topological protection in a certain class. Namely, unless the symmetry is broken, the topological nature is intact. We show novel interplay phenomena between symmetry and topology in topological phase transitions associated with line-nodal superconductors. The interplay may induce an exotic universality class in sharp contrast to that of the phenomenological Landau-Ginzburg theory. Hyper-scaling violation and emergent relativistic scaling are main characteristics, and the interplay even induces unusually large quantum critical region. We propose characteristic experimental signatures around the phase transitions in three spatial dimensions, for example, a linear phase boundary in a temperature-tuning parameter phase-diagram.Comment: 4 + 23 pages, 7 figures, 1 table; the first two authors contributed equally to this wor

Distinctive-attribute Extraction for Image Captioning

Image captioning, an open research issue, has been evolved with the progress of deep neural networks. Convolutional neural networks (CNNs) and recurrent neural networks (RNNs) are employed to compute image features and generate natural language descriptions in the research. In previous works, a caption involving semantic description can be generated by applying additional information into the RNNs. In this approach, we propose a distinctive-attribute extraction (DaE) which explicitly encourages significant meanings to generate an accurate caption describing the overall meaning of the image with their unique situation. Specifically, the captions of training images are analyzed by term frequency-inverse document frequency (TF-IDF), and the analyzed semantic information is trained to extract distinctive-attributes for inferring captions. The proposed scheme is evaluated on a challenge data, and it improves an objective performance while describing images in more detail.Comment: 14 main pages, 4 supplementary page

LAD Asymptotics under Conditional Heteroskedasticity with Possibly Infinite Error Densities

Least absolute deviations (LAD) estimation of linear time-series models is considered under conditional heteroskedasticity and serial correlation. The limit theory of the LAD estimator is obtained without assuming the finite density condition for the errors that is required in standard LAD asymptotics. The results are particularly useful in application of LAD estimation to financial time series data.Asymptotic leptokurtosis, Convex function, Infinite density, Least absolute deviations, Median, Weak convergence

Infinite Density at the Median and the Typical Shape of Stock Return Distributions

Statistics are developed to test for the presence of an asymptotic discontinuity (or infinite density or peakedness) in a probability density at the median. The approach makes use of work by Knight (1998) on L_1 estimation asymptotics in conjunction with non-parametric kernel density estimation methods. The size and power of the tests are assessed, and conditions under which the tests have good performance are explored in simulations. The new methods are applied to stock returns of leading companies across major U.S. industry groups. The results confirm the presence of infinite density at the median as a new significant empirical evidence for stock return distributions.Asymptotic leptokurtosis, Infinite density at the median, Least absolute deviations, Kernel density estimation, Stock returns, Stylized facts